The determination of the analytical solution of the Euler's angles [1]} is essential to stipulate the motion of the body in relation to an inertial frame of reference. Thus it is an essential result to obtain the motion of Poinsot's geometric solution [2]}. As the position of the coordinate axes fixed in space is arbitrary, a coordinate system will be chosen such that the \(Z\)  axis contains the invariant angular momentum vector \(\overrightarrow{H}_{o}\) , also it will be considered a null initial precession angle \(\psi _{0}\) .
